The present invention relates to image processing systems and methods, and more particularly to image registration systems that combine two or more images into a composite image.
Image registration involves combining two or more images, or selected points from the images, to produce a composite image containing data from each of the registered images. During registration, a transformation is computed that maps related points among the combined images so that points defining the same structure in each of the combined images are correlated in the composite image.
Currently, practitioners follow two different registration techniques. The first requires that an individual with expertise in the structure of the object represented in the images label a set of landmarks in each of the images that are to be registered. For example, when registering two MRI images of different axial slices of a human head, a physician may label points, or a contour surrounding these points, corresponding to the cerebellum in two images. The two images are then registered by relying on a known relationship among the landmarks in the two brain images.
The mathematics underlying this registration process is known as small deformation multi-target registration. In the previous example of two brain images being registered, using a purely operator-driven approach, a set of N landmarks identified by the physician, represented by x.sub.i, where i=1 . . . N, are defined within the two brain coordinate systems. A mapping relationship, mapping the N points selected in one image to the corresponding N points in the other image, is defined by the equation u(x.sub.i)=k.sub.i, where i=1 . . . N. Each of the coefficients, k.sub.i, is assumed known.
The mapping relationship u(x) is extended from the set of N landmark points to the continuum using a linear quadratic form regularization optimization of the equation: ##EQU1## subject to the boundary constraints u(x.sub.i)=k.sub.i. The operator L is a linear differential operator. This linear optimization problem has a closed form solution. Selecting L=.alpha..gradient..sup.2 +.beta..gradient.(.gradient..) gives rise to small deformation elasticity. For a description of small deformation elasticity see S. Timoshenko, Theory of Elasticity, McGraw-Hill, 1934 and R. L. Bisplinghoff, J. W. Marr, and T. H. H. Pian, Statistics of Deformable Solids, Dover Publications, Inc., 1965. Selecting L=.gradient..sup.2 gives rise to a membrane or Laplacian model. Others have used this operator in their work, see e.g., Amit, U. Grenander, and M. Piccioni, "Structural image restoration through deformable templates," J. American Statistical Association. 86(414):376-387, June 1991, and R. Szeliski, Bayesian Modeling of Uncertainty in Low-Level Vision, Kluwer Academic Publisher, Boston, 1989 (also describing a bi-harmonic approach). Selecting L=.gradient..sup.4 gives a spline or biharmonic registration method. For examples of applications using this operator see Grace Wahba, "Spline Models for Observational Data," Regional Conference Series in Applied Mathematics. SIAM, 1990, and F. L. Bookstein, The Measurement of Biological Shape and Shape Change, volume 24, Springer-Verlag: Lecture Notes in Biomathematics, New York, 1978.
The second currently-practiced technique for image registration uses the mathematics of small deformation multi-target registration and is purely image data driven. Here, volume based imagery is generated of the two targets from which a coordinate system transformation is constructed. Using this approach, a distance measure, represented by the expression D(u), represents the distance between a template T(x) and a target image S(x) The optimization equation guiding the registration of the two images using a distance measure is: ##EQU2##
The distance measure D(u) measuring the disparity between imagery has various forms, e.g., the Gaussian squared error distance .intg..vertline.T(h(x))-S(x).vertline..sup.2 dx, a correlation distance, or a Kullback Liebler distance. Registration of the two images requires finding a mapping that minimizes this distance.
One limitation of the first approach to image registration is that the registration accuracy depends on the number and location of landmarks selected. Selecting too few landmarks may result in an inaccurate registration. Selecting too many landmarks does not necessarily guarantee accurate registration, but it does significantly increase the computational complexity of registration. Furthermore, it is not always possible to identify appropriate structural landmarks in all images.
The second technique is limited by the computational complexity presented by the number of data points in most images. The second technique is further limited by the fact that the process produces many local minima that confuse proper registration. This is because when registering two images according to the second technique, many possible orientations of the images produce subregions in the images that are properly matched, but the images as a whole are improperly registered.
There is, therefore, a need for a registration technique that overcomes the limitations of the conventional techniques.